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F test notes

posted Dec 3, 2010, 7:07 PM by Prof Kiernan   [ updated Dec 3, 2010, 7:39 PM ]

You can use the F test to verify a claim about a standard deviation (or variance) for 2 data sets.

Assumptions: The sample is from a "normal distribution"

NOTE: some professors prefer to use the following notation: N~(mean, Standard Deviation)

English Translation: Use an F test  if you are Given: 2 sample sizes (n) and 2 standard deviations (or variances=s2 ) AND you are testing a claim about a standard deviation or variance.

Writing the hypothesis:

H0population standard deviation1 = population standard deviation2

H1: population standard deviationis less than, greater than, or not equal to population standard deviation2

Critical Value = shaded area from F table using the degrees of freedom.

Degrees of freedom: for numerator (use the info from the bigger Standard Deviation) n-1, for denominator (use the info from the smaller Standard Deviation) n-1. Remember that if the null hypothesis requires two tails, split the alpha before using the tables.

Test statistic formula:

F = variance1 / variance2

**The bigger variance (standard deviation squared) must be divided by the smaller variance (standard deviation squared).**


Press STAT

Highlight TESTS

Select 2-SampFTest 

Put your information in.

    **NOTE: S1 must be the biggest standard deviation**

Make sure the not equal to, less than, or greater than symbol matches the one in your alternative hypothesis (H1).

Highlight Calculate Press ENTER

F is the test statistic, and P is the P-value.

Rejection of the null hypothesis (Ho):

You can reject the null hypothesis if:

  • the F from the formula falls in the shaded critical area from the table.
  • the P-value is smaller than your alpha Reject Ho.

Remember: if you are not given an alpha assume you are using 0.05.